※ 引述《yabt (痴心絕對)》之銘言：
: The following is just my guess, it may not be correct :)
Thank you very much.
Your explanation is quite clear and useful.
: Note that some functions of the samples T(X1, X2, ..., Xn) would follow the
: sample distribution of T(X) no matter with or without replacement, where
: X1~Xn are random variables of the samples, and X is the real random variable
: of the underlying model. The average function T = sum(Xi)/n is a good example.
: There are also some functions such that their distributions are not the same,
: for instance, T(X) = X2, the transform that we only keep the result of the
: second sample.
May I ask one more question?
I do not understand the description,
"soe functions of the the samples T(X1, X2, ..., Xn) would follow
the sample distribution of T(X)".
Does that mean T(X1, X2, ..., Xn) will reflect the real distribution of T(X)?
Is there any definition or rule to decide whether one distribution is
following another one?
Thank you for your responses and all your time.
: What's more, consider the case that the size of the data is large. The former
: sample from, say 1000:1000, will not affect the probability distribution of
: the later sample that much, say 1000:999. That's why sampling without
: replacement is OK only if we have a large data set.